{
  "annotation_id": "1193f819-0dda-4705-a4b7-c5a6f1e8b096",
  "date_created": "2026-03-02T18:02:17.285000Z",
  "date_modified": "2026-03-02T18:02:17.285000Z",
  "file_hash": "fc43c2ef3e31f4604ef00d22b10f8cb92401bca2f6a1070a79c33e8b42e0e1ff",
  "private": false,
  "record": {
    "abstract": "We consider the problem of testing the commutativity of a black-box group\nspecified by its k generators. The complexity (in terms of k) of this problem\nwas first considered by Pak, who gave a randomized algorithm involving O(k)\ngroup operations. We construct a quite optimal quantum algorithm for this\nproblem whose complexity is in O (k^{2/3}). The algorithm uses and highlights\nthe power of the quantization method of Szegedy. For the lower bound of\nOmega(k^{2/3}), we give a reduction from a special case of Element Distinctness\nto our problem. Along the way, we prove the optimality of the algorithm of Pak\nfor the randomized model.",
    "arxiv_id": "quant-ph/0506265",
    "authors": [
      "Frederic Magniez",
      "Ashwin Nayak"
    ],
    "categories": [
      "quant-ph",
      "cs.DS"
    ],
    "title": "Quantum Complexity of Testing Group Commutativity",
    "url": "https://arxiv.org/abs/quant-ph/0506265"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3662f48f-2a39-4160-ade2-cad50a6c3e92",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}